# Эксперимент: Kac-Ward Exact Teacher for Autoregressive Samplers (#1052)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a tiny planar-Ising autoregressive distillation MVP with exact conditional probabilities by enumeration and a Kac–Ward determinant sanity check. The CE-minus-entropy equals conditional-KL identity held with absolute error below 7e-17, and the half-angle Kac–Ward formula matched enumeration to 1.9e-15 relative error on 3x3. Soft oracle supervision consistently improved conditional KL over sampled-label training, confirming the proposed mechanism in this toy setting.",
  "metrics": {
    "baseline": "Sampled-label conditional KL: 0.02115, 0.03466, 0.03366 at beta 0.2, 0.7, 1.3.",
    "idea": "Soft-oracle conditional KL: 0.0000680, 0.000333, 0.00138 at beta 0.2, 0.7, 1.3; approximately 25x–311x lower than baseline."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "kw_test.py"
  ],
  "limitations": "The conditional oracle uses brute-force enumeration rather than the paper’s auxiliary-graph conditional Kac–Ward construction, so this is only a small-lattice MVP. It does not test 6x6 or larger instances, held-out generalization, replay-based active correction, observables, autocorrelation, or the claimed O(N^{5/2}) Kac–Ward scaling."
}